Hydraulics Laboratory Experiment Report

Transcription

1 Hydraulics Laboratory Experiment Report Name: Ahmed Essam Mansour Section: "1", Monday 2-5 pm Title: Impact of a Jet Date: October 9, 2006

2 Objectives: Study the relation between the force produced and the change of momentum when a jet strikes a vane. Compare between force exerted by a jet on a flat plate and on a hemispherical surface. Theory: In order to calculate the force caused by impact of a jet into a flat plate or curved vane, the change in momentum principle is applied; Force = Rate of change in momentum F = ρ Q ΔV F = ρ Q (V in V out ) Where; F: the force exerted by the jet on the plate. ρ: the mass density of water (= 1000 kg/m 3 ). Q: volumetric rate of flow (m 3 /s). ΔV: the change in velocity just after and before impact. The volumetric flow rate in the equation 'Q' is calculated in the experiment by taking an amount of volume in a known period of time and then use; Q = v / t V in is calculated in the experiment by first knowing the velocity at the nozzle and then using the motion equations. V nozzel is measured by know the diameter of the nozzle (dia = 10mm) and the volumetric flow rate 'Q' calculated previously, V nozzel = Q/ A

3 Then V in is calculated by; V in 2 = V nozzel 2 2 g S Where; g: the gravitational acceleration (9.81 m/s 2 ). S: the distance between the jet and the plates (35mm) V out generally equals V in cos θ, where θ represents the change in direction of the jet. For the flat plat θ = 90, so that V out = 0.0. For the Hemispherical cup θ = 180, so that V out = -V in So the following relations are used for calculating the Predicted values of the force; For the Flat plate: For the Hemi spherical cup: F = ρ Q V in F =2 ρ Q V in The measured force from the experiment is calculated by using the equilibrium of moment equation. And the final relation for calculating the measured force is; F = 4 * 9.81 * d Where 'd' is the ruler reading for the jockey weight.

4 Apparatus: This apparatus is designed primarily for use on the TQ H1 or H1D Hydraulics Bench. By directly measuring the force exerted on the plates by the water jet, it allows the student to experimentally study the theoretical momentum laws used to solve jet impact problems. An upper weigh beam is pivoted on precision bearings at one end and carries along its length the fixed test plate. The beam jockey and a scale are used to measure the jet force. An adjustable spring supports the lever and is used for setting the initial zero level of the beam. A hanging tally weight on the end of the beam is used to return the beam to horizontal each time a reading is required. A high velocity jet is produced by the vertical tapered nozzle. For clear observation, both nozzle and test plate are contained in a transparent cylinder. The apparatus is leveled for test using the plastic screwed ball feet provided on the base legs. A drain tube, in the base of the cylinder vessel, is used to direct the water to the weigh tank of the H1 or H1D Bench where the flow can be accurately measured. Procedures: 1. The lever was set to is balanced position with the jockey weight is at its zero position. 2. The water valve was opened to it max, and the jockey was repositioned so that the lever is back to its balanced position.

5 3. The water tank was emptied of water and the refilled to take reading of time versus volume which was used to calculate the volumetric rate of flow. 4. A series of reading for the similar procedures was taken for the flat plate with reducing the rate of flow in each reading by using the valve. 5. The same steps were then repeated by using the hemispherical cup instead of the flat plate. Results: Data: Volume (liters) Time (seconds) d (mm) Q V nozzel (m 3 /s) * 10-4 (m/s) V in (m/s) F 1 Predicted (N) F 2 Measured (N) Flat Plate Hemispherical Cup (Plots are plotted by using MATLAB 7)

6 Sample of calculations:

7 Conclusions: From the results obtained and the plots graphed, the following points were concluded: As the volumetric rate of flow 'Q' increased, the force resulted from the impact of the jet on both the flat plate and the hemispherical cup, is increased to for the predicted 'F 1 ' and the measured 'F 2 ' values of the force. This relation can be seen clearly from the four plots accompanied with this report. This result was already predicted from the change in momentum equation of calculating the force. The predicted value of the Jet force showed larger values than the measured one. This might be occurred for the following reasons: o Errors in taking the reading. o Losses in the experiment apparatus. These losses were used in calculating the experiment efficiency which showed values of 0.8 for the flat plate and 0.83 for the hemispherical cup. The impact of the Jet forces on the flat plate where half of it on the hemispherical cup. This result is displayed clearly in plots 1 & 2 for both predicted and measured values of the force. This was already predicted from the equations of momentum for calculating the forces. According to the last point the hemispherical cup is more efficient for using in a turbine than the flat plat, but only one point to be considered is that the water to exit the cup is going to collide with water entering the cup which will reduce the force, for that reason the cup is made in angles less than 180.